Estimate how high the dam should be in order for the power of the hydroelectric power station to be enough for

Estimate how high the dam should be in order for the power of the hydroelectric power station to be enough for Evaporation of all the water passing through its turbines? The temperature of the water in the river is considered equal to 20c, the specific heat capacity of water is 4 kJ / kg. Specific heat of vaporization of water 2.3 mJ / kg

In order for water to evaporate, it must first be heated to its boiling point, up to 100 degrees Celsius, we calculate by the formula for finding the amount of heat needed to heat bodies: Q = m * c * dt;

Then it is necessary to evaporate all this water heated to the boiling point, calculation by the formula: Q = L * m;

Let’s combine the formulas and get:

m * g * h = c * m * dt + L * m;

From this formula, we express the height h:

h = (c * dt + L): g

h = (4 * 10 ^ 3 * 80 + 2.3 * 10 ^ 6): 10 = 2.62 * 10 ^ 5 = 262 km